Finite-Time Distributed Control for Heterogeneous Signed Networks

This study explores the finite-time distributed control problem in heterogeneous signed networks. In scenarios where the velocity of second-order networks are unobservable, this research designs a nonlinear control protocol by introducing auxiliary variables and relative displacement information. This protocol enables heterogeneous signed networks with undirected topology to achieve bipartite consensus within a finite time under structurally balanced conditions and reach state stability within a finite time when structurally unbalanced. The effectiveness of this protocol is proven using methods such as the Lyapunov stability theorem and graph theory. Moreover, the validity of the theoretical result is confirmed through simulation experiments.